2a2+5a-25=0
-5 and 5/2 are both correct answers
To solve the quadratic equation 2a^2 + 5a - 25 = 0, you can use the quadratic formula. The quadratic formula states that for any quadratic equation in the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In the case of your equation, the coefficients are a = 2, b = 5, and c = -25.
Substituting these values into the quadratic formula, we get:
a = 2, b = 5, c = -25
x = (-5 ± √(5^2 - 4(2)(-25))) / (2(2))
Simplifying further:
x = (-5 ± √(25 + 200)) / 4
x = (-5 ± √225) / 4
x = (-5 ± 15) / 4
Simplifying the two possible solutions:
x1 = (-5 + 15) / 4 = 10 / 4 = 2.5
x2 = (-5 - 15) / 4 = -20 / 4 = -5
Therefore, the quadratic equation 2a^2 + 5a - 25 = 0 has two solutions: a = 2.5 and a = -5.